Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of Dic30 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic30 |
| Hall | C3×C5×C11 ⋊ Q8 |
| Hall | C5×C11 ⋊ Dic6 |
| Hall | C3×C11 ⋊ Dic10 |
| Hall | C3×C5 ⋊ Q8×C11 |
| Sylow | C5 ⋊ C11×Dic6 |
| Sylow | C3 ⋊ C11×Dic10 |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 1320 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,19,18,17)(20,21,22)(23,24,25,26,27);(12,16,14,18)(13,17,15,19)(21,22)(24,27)(25,26)363 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 120);